The story goes that donkeys are very stubborn and their owners have great trouble getting them to move. Eventually, they found a solution that worked: dangling a carrot from a stick in front of the donkey. Donkeys not being too smart, see the carrot and start moving towards it. That is, the dangling carrot is being used to motivate the donkey. The same idea can be applied to people, but we don't normally use carrots, perhaps a promotion, a holiday, a nice meal.

Quote:

She was very concened about the speeches he was making and dangled carrots in fornt of his nose to try to shut him up.

In your example, she's trying to distract the speaker by offering something - we don't know what, but it must be nice.

Iain_________________
Teachers open the door, but you must enter by yourself.
--Chinese Proverb